In the figure shown, each tiny ball has mass m, and the string has length L. One of the balls is imparted a velocity u , in the position shown, in which the intial distance between the balls is 4 3 L

Question

In the figure shown, each tiny ball has mass m, and the string has length L. One of the balls is imparted a velocity $u$ , in the position shown, in which the intial distance between the balls is $\frac{3 L}{4}$ . If the impulse of the tension in the string when it becomes taut is $m α kg - ms^{- 1}$ , then find the value of $α$ .

TestHub · Accepted Answer

Taut when the separation becomes L. With $cos 5 3^{\circ} = 0.6, sin 5 3^{\circ} = 0.8$ : $(0.75 L + 0.6 s)^{2} + (0.8 s)^{2} = L^{2} \Rightarrow s = 0.35 L$ , where s = ut.

Geometry then gives the velocity's component along the string = 0.8u; the tension impulse equalises the along-string components of the two equal masses:

$J = m \times \frac{0.8 u}{2} = 0.4 m u = 0.4 \times 15 = 6$

Ans. 6

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